This specification relates to statistical machine translation.
Manual translation of text by a human operator can be time consuming and costly. One goal of machine translation is to automatically translate text in a source language to corresponding text in a target language. There are several different approaches to machine translation including example-based machine translation and statistical machine translation. Statistical machine translation attempts to identify a most probable translation in a target language given a particular input in a source language. For example, when translating a sentence from French to English, statistical machine translation identifies the most probable English sentence given the French sentence. This maximum likelihood translation can be written as:
            arg      ⁢                          ⁢      max        e    ⁢          ⁢      P    ⁡          (              e        ❘        f            )      which describes the English sentence, e, out of all possible sentences, that provides the highest value for P(e|f). Additionally, Bayes Rule provides that:
      P    ⁡          (              e        ❘        f            )        =                              P          ⁡                      (            e            )                          ⁢                  P          ⁡                      (                          f              ❘              e                        )                                      P        ⁡                  (          f          )                      .  Using Bayes Rule, this most likely sentence can be re-written as:
                    arg        ⁢                                  ⁢        max            e        ⁢                  ⁢          P      ⁡              (                  e          ❘          f                )              =                    arg        ⁢                                  ⁢        max            e        ⁢                  ⁢          P      ⁡              (        e        )              ⁢                  P        ⁡                  (                      f            ❘            e                    )                    .      
Consequently, the most likely e (i.e., the most likely English translation) is one that maximizes the product of the probability that e occurs and the probability that e would be translated into f (i.e., the probability that a given English sentence would be translated into the French sentence).